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• An earthquake is caused by sudden movement on a sub-surface fault. The energy which is released (which was stored as strain in the rock) is converted to seismic waves which radiate from the earthquake focus. These seismic waves cause ground shaking and can be measured using seismometers.
• This session focuses on the seismic waves that result from an earthquake.
• Two categories of seismic wave exist – body waves (which travel through the entire volume of the Earth) and surface waves (which are restricted to the near-surface). Each category consists of several types of seismic wave which all propagate through the earth with different velocity, amplitude, and particle motion.
• Body waves are those which travel through the entire volume of the Earth. There are two types: P-waves (Primary, or first arriving) are the quickest and have a compressional particle motion parallel to the direction of travel. S-waves (Shear) are quicker than surface waves, and have a shearing particle motion perpendicular to the direction of travel. The velocity of a P or S wave is related to the bulk or shear moduli (respectively) of the material through which they travel.
• Different arrivals in a seismic wave-train can usually be identified by considering the particle motion of each seismic wave.
• Surface waves are those which are restricted to propagation close to the free surface. There are two main types: Love waves have a shearing particle motion but only in the horizontal plane (parallel to the ground surface). Rayleigh waves have a reverse retrograde ellipse particle motion parallel to the direction of propagation.
• On a 3-component seismometer we can separate out the Love and Rayleigh waves as a result of their different particle motion. The Love waves arrive earlier. A seismometer records the ground motion caused by the different seismic waves as they arrive and pass by. Different records are made in 3 orthogonal directions – N, E, and Z. Depending on the distance to the source, different ‘phases’ (the recorded waveforms corresponding to different seismic arrivals) could appear close together in a complicated wave-train (if the earthquake was close), or separated out into distinct arrivals depending on the propagation velocity of each seismic wave. If the earthquake was very far away (Teleseismic) then surface waves will not be recorded.
• In the spatial domain, one wavelength describes the distance for one complete cycle of the seismic wave (e.g. peak to peak, or trough to trough). In the time domain, the period describes the time taken for one whole cycle to pass a certain point/ The velocity of the wave is related to both the wavelength and the period.
• The different phases have different wavelengths and periods, this is important when we try to use the seismic waves to investigate the earthquake source – see earthquake sources lecture.
• Depending on the geometry of the ray path of a particular seismic wave as it hits a seismic discontinuity (boundary over which the velocity differs) it could be refracted or reflected, or even converted from a P- to an S-wave (or vice versa). As a result, many different seismic phases can be recorded which have taken different paths through the earth to get from the source to the seismometer, and have different travel-times.
• Seismic waves travel through the Earth according to the laws of optics. Snell’s law, as illustrated here, describes the refraction of a seismic ray as it crosses a velocity contrast
• When velocity increases with depth within the Earth the rays a refracted back towards the Earth’s surface (left hand example), when the velocity decreases within the earth the rays are refracted away from the surface (right hand example).
• With several layers of increasing velocity this effect is repeated. The time taken for the ray to travel from the source to the receiver is the sum of the distance traveled in each layer multiplied by the velocity of that layer. If we have a number of recording stations in a simple patch of ground and we plot the time of arrival against the distance from the source we create a plot like the one on the right. In a constant velocity layer the time taken is proportional to the distance traveled and the graph is a straight line (giving the velocity of the layer). We investigate the structure of the earth using this – by recording the arrival times at many locations we can create a plot similar to the one on the right (but more complicated) and use this to try and calculate the velocity structure of the earth.
• The Moho is a good example of a seismic discontinuity across which seismic velocity is different. Andrija Mohorovicic found a very sharp change in velocity within the earth in Croatia, which was later shown to occur everywhere at varying depths (average of about 40 km under the continents and ~7 km below the seabed under the oceans). The velocity change is interpreted to happen at the boundary between crustal material and mantle material, and is known as the Moho after Mohorovicic.
• The Earth has a complicated structure. The changes in velocity with depth result in refraction and reflection of the seismic energy. So the ray paths through the Earth are complicated.
• Ray paths through the mantle are relatively simple. There are a few changes associated with the 410 and 660 km discontinuities, but nothing compared to the deeper earth.
• Because the outer core is a liquid, S waves do not propagate through it (this is because a liquid cannot support shearing) and P waves are slower. So the ray that enters the inner core bends away from the surface, deeper into the earth.
• Steeper incident rays are less affected and so we end up with deeper ray paths arriving nearer the source.
• We then have another short forward branch. However, no direct P energy arrives in a zone ~105-~143 degrees from the source – the shadow zone because of the refractive properties of the mantle-core boundary.
• A time-distance plot through the mantle shows this complexity.
• PcP is an example of a P phase which has reflected off the core-mantle boundary because it’s angle of incidence at the boundary is greater than the critical angle.
• There are many possible ray paths within the earth, all of which have been observed. Phases are named according to their path through the Earth. For instance a P wave which travels directly through the centre of the Earth is called the PKIKP phase
• Collation of recorded phase data. Blue represents the vertical component.
• The intensity of earthquake shaking is directly related to the amplitude of the seismic waves. The above relationship describes the decay of amplitude with distance.
• Normal modes are the free oscillations of the Earth that happen following a large earthquake – they are similar to the ringing of a bell. They have much longer periods and wavelengths than other seismic waves so they are very useful for studying the largest earthquakes. Like a bell there are initially many different frequencies, but the higher modes attenuate (lose amplitude) more rapidly than the lower modes, so with time the ringing simplifies.
• Some of the more simple and longer period ways the earth can oscillate. The top figure on the right is known as the “breathing mode” as the Earth expands and contracts. The lower figure is the “football mode” . Note that these waves have periods of many 10’s of minutes , far longer than P, S and surface waves.
• More ways the earth can oscillate.
• ### Caribbean3

1. 1. Seismic Waves An introduction Walter D. Mooney,USGS Menlo Park, CA.
2. 2. What is an Earthquake? • Instrumentally recorded (or felt) ground shaking, normally a result of underground movement on a faultSeismogram of the 1906 earthquakerecorded in Germany San Francisco 1906 (USGS)
3. 3. Faulting Seismic wavesUSGS
4. 4. Types of Seismic Wave Three-components of a seismometer record proportional to ground velocity of the P and S waves from a local aftershock of the Killari-Latur EQ, India (1993), at a hypocentral distance of 5.3 km P. Bormann. 2002. New Manual of Seismological Observatory Practice (NMSOP)
5. 5. Body Waves P. Bormann, NMSOP Bulk modulus κ = ∆P / (∆V/ V) ⇒ Shear modulus λ + 2µ κ + 4µ / 3 or „rigidity“vp = = µ = (∆F/A) / (∆L/L) ⇒ ρ ρ Young´s or „stretch“ modulus E = (F/A)/ (∆L/L) and Poisson ratio σ = (∆W/W) / (∆L/L) ⇒ µ vp Deformation of materialvs = samples for determining ρ = 3 elastic moduli vs © Copyright 2004. L. Braile.
6. 6. Particle motion of body waves < 4.5 s > 1s3-component records at station MOX (top traces) and related plots of particle motion in the horizontal (N - E) planeand two vertical planes (Z - N and Z – E, respectively) of the P- wave onset from seismic event (mining collapse) inGermany (1989; Ml = 5.5; epicentral distance D = 112 km, back-azimuth BAZ = 273°). Left: broadband recording(0.1 – 5 Hz); right: filtered short-period recording (1 – 5 Hz). Note: The incidence angle is 59.5° for the long-period P- wave oscillation and 47.3° for the high-frequency P-wave group. P. Bormann (NMSOP)
7. 7. Surface Waves– Form at the free surface– Amplitude decays exponentially with depth. © Copyright 2004. L. Braile.
8. 8. January 26, 2001 Gujarat, India Earthquake (Mw7.7) vertical Rayleigh Waves radial transverse Love Waves Recorded in Japan at a distance of 57o (6300 km) Courtesy J. Mori
9. 9. Wave Period and Wavelength 　 Velocity 6 km/sSpace x wavelength 300 km wavelength 　　Time t period 50 s frequency = 1/period= 0.02 Hz period Velocity = Wavelength / Period Courtesy J. Mori
10. 10. Period WavelengthBody waves 0.01 to 50 sec 50 m to 500 kmSurface waves 10 to 350 sec 30 to 1000 kmFree Oscillations 350 to 3600 sec 1000 to 10000 kmStaticDisplacements ∞ - Courtesy J. Mori
11. 11. Other phasesDigital broadband record of the Seattle Mw = 6,8 earthquake on 28 February 2001 atthe station Rüdersdorf (RUE) in Germany (epicentral distance D = 73°). Note thedetailed interpretation of secondary phase onsets. P. Bormann (NMSOP)
12. 12. Ray theory• Seismic waves can be represented as rays
13. 13. Ray Paths in a Layered Medium sin θ1 / α1 = sin θ2 / α2 = s1 sin θ1 = s2 sin θ2 α = velocity of seismic energy in the layer α1 θ1 slower α1 θ1 Faster θ2 Faster θ2 Slower α2 α2 α1 < α2 α1 > α2 Courtesy J. Mori
14. 14. Ray Paths in a Layered Medium Time 1/α3 1/α2 1/α1 Distanceα1α2α3 Courtesy J. Mori
15. 15. The Moho Andrija Mohorovicic (1857-1936) Found seismic discontinuity at 30 km depth in the Kupa Valley (Croatia). Mohorovicic discontinuity or ‘Moho’ 　 Boundary between crust and mantleThe Moho The Moho Copywrite Tasa Graphic Arts
16. 16. Structure in the Earth results in complicated paths Lowrie, 1997, fig 3.69 USGS Bolt, 2004, fig 6.3
17. 17. Propagation of Seismic Waves In the Earth; M. Wysession
18. 18. Courtesy R. MereuCourtesy J. Mori
19. 19. Courtesy J. Mori
20. 20. Forward BranchBackward Branch Courtesy J. Mori
21. 21. Forward Branch Shadow Zone Forward BranchBackward Branch Courtesy J. Mori
22. 22. PcP Backward Branch Forward PKP Branch Forward Branch Shadow PcP Shadow Zone P Zone Forward Branch Backward Branch Forward Branch・ 1912 Gutenberg observed shadow zone 105o to 143o・ 1939 Jeffreys fixed depth of core at 2898 km (using PcP) Courtesy J. Mori
23. 23. PcPCore Reflections Courtesy J. Mori
24. 24. P Mantle P S Mantle S K Outer core P I Inner core P c Reflection from the outer core i Reflection from the inner core diff Diffracted arrivalIASP91, Kennett and Engdahl, 1991
25. 25. Stacked broadbandseismograms for shallowearthquakes. Seismicphases are shown indifferent colors:Blue = verticalGreen = radial horizontalRed = transverse horizontal P. Bormann. 2002. New Manual of Seismological Observatory Practice (NMSOP)
26. 26. Amplitude and Intensity Seismic waves lose amplitude with distance traveled - attenuation A(t) = A0e -ω0t/2QSo the amplitude of thewaves depends on distancefrom the earthquake.Therefore unlike magnitudeintensity is not a singlenumber.
27. 27. Normal ModesLiberty Bell (USA) Useful for studies of ・ Interior of the Earth ・ Largest earthquakes l=1 m=1 l=1 m=2 l=1 m=3 Houseman http://earth.leeds.ac.uk/~greg/?Sphar/index.html
28. 28. Toroidal and Spheroidal ModesToroidal Spheroidal Dahlen and Tromp Fig. 8.5, 8.17
29. 29. Natural Vibrations of the Earth Shearer Ch.8.6 Lay and Wallace, Ch. 4.6